Pith. sign in

REVIEW 3 major objections 5 minor 71 references

Resolving Speed and Encoding Bottlenecks in Fast Heteromeric Self-Assembly

T0 review · 3 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A single extra bond per layer resolves both the speed and encoding bottlenecks of quasi-2D heteromeric self-assembly, by raising the critical layer-nucleation events from one to two bonds and yielding an encoding capacity that scales as N^{

desk verdict A kinetic-encoding model with a genuinely nice bottleneck mechanism; the central capacity scaling rests on a heuristic count that needs shoring up before the strong claims are accepted. read the letter →

arxiv 2511.16362 v2 pith:MWORPKVE submitted 2025-11-20 cond-mat.stat-mech

Félix Benoist , Pablo Sartori This is my paper · ORCID
classification cond-mat.stat-mech
keywords kineticencodingself-assemblyheteromericcomplexesassemblyfactorsspeed-accuracytradeoffcapacityconnectivitybottlenecks
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper studies a simplified model of how large multi-protein complexes assemble quickly and reliably from a crowded mixture. The authors encode target structures purely in reaction kinetics, not binding energies: monomers bind faster when they match a local neighborhood of a target. They show that in a two-dimensional lattice model, the slowest growth step—nucleating a new layer with only one bond—also becomes the step where wrong components cannot be distinguished, so speed and accuracy fail together. Their central result is that adding a single extra bond per layer, so that layer nucleation creates two bonds instead of one, removes both bottlenecks at once, with negligible change to average connectivity. They further show that increasing connectivity to three bonds per critical event raises the number of structures that can be encoded simultaneously from a constant to a power of the system size.

What carries the argument

The load-bearing construct is the critical addition event: the growth step with the smallest number of bonds n_c, defined through the mini-max rate k_c = min_t max_{i,x} exp(r_i(N_x) δ). In the irreversible high-discrimination regime, n_c controls three outputs: the retrieval time τ_ret ≈ (N_c/Ω_C) exp(-n_c δ), the discrimination threshold δ_min = (1/n_c) ln(N_c Ω_I/Ω_C), and the encoding capacity S_max ~ N^{1-2/n_c}. The capacity scaling follows from a combinatorial count of 'confounding' monomers that share n_c correct partners with the intended one, estimated as N_I ~ (S-1)^{n_c} / N^{n_c-1} under the assumption that target rearrangements are random. Increasing local connectivity—one extr

What would settle it

Measure the maximum number of codable structures Smax for a fixed system size N under controlled target sets: with targets engineered to share correlated motifs (e.g., repeated sub-neighborhoods), the capacity should fall below the predicted N^{1-2/nc}; conversely, with random reshufflings it should match. A second test: for z=4+, the retrieval time should scale as τret ~ N exp(-2δ); if the measured δ-dependence instead remains exp(-δ), the extra bond has not actually raised the critical bond number, falsifying the bottleneck-suppression mechanism.

Watch

Extended reading notes

Core claim

The paper's central claim is that, in quasi-2D heteromeric self-assembly with kinetic encoding, the critical events that limit assembly speed are the same events that limit encoding accuracy: the nucleation of new layers, where a monomer attaches with a single bond (nc = 1). With nearest-neighbor-only connectivity (z = 4), these events slow retrieval time to τret ≈ exp(-δ) and cap the number of simultaneously encodable structures at Smax = 1. Adding one diagonal bond per layer (z = 4+, only 2ℓ of N components affected) lifts the critical bond number to nc = 2, making retrieval exponentially faster, τret ≈ N exp(-2δ), and eliminating combinatorial errors for a few targets. More generally, for

Load-bearing premise

The central scaling law Smax ~ N^{1-2/nc} rests on treating the set of target structures as independent random reshufflings when counting how many wrong monomers share n_c bonds with the correct one (SI Sec. S4, Eq. S11); if real targets are correlated in their neighborhoods, the predicted capacity scaling would not hold.

Editorial extensions

If this is right

  • If correct, the model predicts an exponential speedup in assembly time (from exp(-δ) to exp(-2δ) or exp(-3δ)) from a connectivity change affecting only O(√N) of N components.
  • It predicts that encoding capacity scales as a power of system size once critical events create at least two bonds: S_max ~ N^{1/3} when three bonds per critical event are enforced.
  • It identifies combinatorial (not thermal) errors as the fundamental limit on storing multiple structures with shared components, independent of the discrimination energy δ.
  • The mechanism suggests why assembly-factor counts grow with complex size: factors effectively supply local connectivity at critical sites, a role consistent with observed data on ribosomes and other large complexes.
  • It suggests design rules for synthetic self-assembling systems (e.g., DNA tiles): selectively boosting the connectivity of a few components should increase both yield and speed without altering the majority of interactions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The bottleneck identity found here—one-bond events being both the slowest and the least discriminating—may generalize beyond square lattices: in any growth process where the lowest-bond-count step has a combinatorial ambiguity, speed and accuracy will fail together, and adding a bond at that step should decouple them.
  • A testable extension of the paper's logic is to three-dimensional assembly: the critical sites would be nucleation events on faces or edges, and the scaling of S_max with N might change because the surface-to-volume ratio differs; this could connect to experimentally observed assembly-factor distributions in 3D complexes.
  • The random-reshuffling counting in SI Sec. S4 implies that the scaling Smax ~ N^{1-2/nc} should be robust to moderate target overlap, but would break for correlated target sets—this could be probed by designing structures with shared motifs and measuring whether capacity degrades faster than power-law.
  • The paper's kinetic-encoding framework, applied to two structures S=2, predicts a ~50% error plateau at large δ for z=4 that is insensitive to δ; this is a sharp, experimentally falsifiable signature distinguishing kinetic from energetic encoding.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper extends a prior heteropolymer kinetic-encoding model to quasi-2D self-assembly. Components are square tiles with nearest-neighbor bonds and, in some designs, extra diagonal bonds; target structures are encoded not in binding energies but in the kinetics, via rates k^± = exp(r_i δ) and exp(r_i δ − µ), where r_i counts the number of neighbors consistent with any encoded target. Retrieval from a nucleation seed is studied analytically and by Gillespie simulation. The central claims are: (i) for nearest-neighbor connectivity z = 4, layer-nucleation events with a single bond (n_c = 1) create a speed bottleneck τ_ret ≈ exp(−δ) and, for S ≥ 2, an encoding bottleneck with S_max = 1; (ii) adding one diagonal bond per layer (z = 4+) raises n_c to 2, removes both bottlenecks, and gives an O(1) encoding capacity; (iii) for higher connectivity, S_max ∼ N^{1−2/n_c}, with explicit predictions S_max ∼ N^{1/3} at z = 6+ and ∼N^{1/2} at z = 8, summarized by S_max ∼ N^{1−4/z}. The paper also presents a compilation of assembly-factor counts and component connectivities for large protein complexes, and argues that kinetic control of a few critical binding events is a plausible design principle for fast, accurate assembly.

Significance. If the central derivation is sound, the paper offers a parameter-free, falsifiable scaling theory for a nontrivial kinetic-encoding problem in heterogeneous self-assembly. The main predictions—Eqs. (4)–(8)—have no fitted parameters and are checked against Gillespie simulations, which is a genuine strength. The idea that a small number of critical events, rather than bulk connectivity, controls both speed and accuracy is novel and potentially important for understanding assembly factors in ribosome and spliceosome assembly. The empirical Fig. 1 data provide useful biological motivation. However, the quantitative core rests on a combinatorial estimate in SI S4 that is not rigorously derived or directly tested, and the main-text sufficiency claim for the retrieval conditions is contradicted by the SI phase diagram. These issues are load-bearing for the paper's main claims, so the result is not yet established at the level claimed.

major comments (3)
  1. [V.B and SI S3 (Eq. S4)] The main text states 'Conditions µ > 0 and δ > δmin result in accurate retrieval' (Sec. V.B). This is not correct as a general statement: SI Fig. S3C-D and Eq. (S4) show that a substantial part of the nominal region µ>0, δ>δmin is not in the transient-retrieval regime. In particular, above the blue line δ_blue ≈ µ/(r_dis − n_c) growth stalls near the seed size, and between the gray and blue lines the target is recovered without further growth. Thus Eq. (4) is only a lower bound on δ, not a sufficient condition. This is load-bearing because the paper's practical claim is that positive µ and sufficiently large δ guarantee fast, accurate retrieval. The main text should state the full retrieval conditions—including the upper bounds—or explicitly restrict the analysis to the µ≫δ regime used in the main simulations, and justify that the simulation parameters of Figs. 3–6 lie inside the retriev
  2. [SI S4, Eq. (S11); Eq. (6)] The central encoding-capacity scaling S_max ∼ N^{1−2/n_c} (Eq. 6) is derived from the estimate N_I ∼ (S−1)^{n_c}/N^{n_c−1} in Eq. (S11). This estimate treats the n_c required neighbor matches as independent draws, allowing each match to come from a possibly different alternative target. In the actual model, targets are reshufflings of the same N species, the neighbors of a monomer within a single target are drawn without replacement, and a confounding monomer must be a valid component of a complete target. Correlations among the S target permutations are not controlled. Moreover, the condition N_c p_err ≪ 1 concerns the typical or worst-case critical event, while Eq. (S11) is an average estimate. Because Eqs. (6) and (8) are the quantitative core of the paper, this omitted justification is load-bearing. Please provide a derivation for a well-defined random-target ensemble, or directly me
  3. [SI S5, Eq. (S18); Eq. (8)] Equation (8), S_max ∼ N^{1−4/z}, is presented as a general scaling, but it is obtained by replacing the discrete n_c with the continuous approximation n_c ≈ z/2 (Eq. S18). Table II and Eq. (S15) show that n_c, N_c, and Ω_C jump at integer values of the number of extra bonds per layer, producing period-ℓ oscillations (Fig. S8). The fit in Fig. 6G uses only three system sizes and a continuous α = 1−4/z, so it does not establish Eq. (8) as a sharp asymptotic prediction. The paper should state explicitly that Eq. (8) is a coarse-grained interpolation, and use the discrete expressions (S15)–(S17) for quantitative comparisons, or provide a rigorous argument for why the fluctuations average out in the large-N limit.
minor comments (5)
  1. [VII and Table II] The wording in Sec. VII 'To guarantee that n_c = 3, we consider assemblies with a bulk connectivity z = 6' is confusing because Table II lists n_c = 2 for z = 6. Please clarify that the design denoted z = 6+ (not z = 6 itself) ensures n_c = 3, or revise the sentence to avoid the apparent contradiction.
  2. [V] The quantities N_c, Ω_C, and Ω_I are used in the main text before they are defined. Please define them at first use, or add a short table in Sec. V, since the reader otherwise has to go to SI S4 to understand Eq. (4).
  3. [SI S4] The sentence 'We thus recall results from the polymerization study [35]' precedes Eq. (S11), which is not a literal result from that study—it is an extension to 2D neighborhoods with n_c ≥ 2. Please present the derivation explicitly rather than recalling it.
  4. [Fig. 5D] The inset claims S_max shows negligible N-dependence for n_c = 2, but the figure uses only ℓ = 7, 14, 20. Please add more system sizes or error bars to make the O(1) claim visually convincing.
  5. [SI S3] The term 'target lifetime' is defined in the main text as the time to add a few incorrect monomers, while SI S3 uses a related but different notion (time to add an extra monomer chunk). Please align the definitions or explicitly distinguish the two quantities.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction: the paper's predictions are analytic counting results tested by simulation, not fits or definitional identities.

full rationale

The quantitative predictions—δmin in Eq. (4), τret in Eq. (5), Smax in Eq. (6), and emin in Eq. (7)—are derived by counting correct and incorrect addition multiplicities at critical events under the explicitly stated irreversible, high-δ, average-neighborhood assumptions of SI Sec. S4. These quantities are not fitted to simulation outputs: comparisons in Figs. 3C, 5C-D, 6C-D and 6F-G use the predicted expressions as lines or midpoint scalings, and the simulation observables (retrieval time, accuracy, sigmoid midpoint) are measured independently. The key combinatorial estimate NI ∼ (S−1)^nc / N^{nc−1} in Eq. (S11) is presented as an average scaling for random target reshufflings and is not a restatement of the desired Smax; Smax follows from the low-error condition Nc perr ≪ 1. The invocation of Ref. [35] to 'recall' the nc=1 result is a same-group prior result for the analogous polymerization problem, but the 2D extension and the connectivity-dependent geometry (nc, Nc, ΩC in SI Sec. S5) are worked out in this paper and checked numerically. The SI's statement that 'we assume that the assembly follows the seeded target' when approximating KC and KI is a standard self-consistent perturbative estimate of error rates along the correct path, not a definitional identity. No step in the derivation chain reduces to its own input, and no load-bearing claim rests solely on an unverified self-citation.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted to data; μ, δ, S, and N are model inputs. The axioms are the kinetic-rate ansatz, the quasi-2D boundary-growth geometry, random-target reshuffling, and irreversible-growth dominance. No new physical entities are introduced; 'assembly factors' are abstracted into accelerated rates.

assumptions (4)
  • domain assumption Binding/unbinding rates follow Eq. (1): k+ = exp(r_i δ), k- = exp(r_i δ - μ); structures are encoded purely kinetically with no free-energy bias.
    Central model ansatz used throughout; if assembly factors or cooperativity act differently on rates (e.g., saturating, as in SI S3), the predicted scalings are model-specific.
  • domain assumption Growth is boundary-driven from a single nucleation seed on a quasi-2D lattice with periodic vertical boundaries and no bulk nucleation.
    Introduced in Sec. II and SI S2; restricts direct transfer to fully 3D or off-lattice assembly where layer-by-layer growth is not enforced.
  • domain assumption Target structures are random independent reshufflings of the N species; component reuse means promiscuity increases uniformly with S.
    Used for the combinatorial counting of confounding monomers in SI S4 Eq. (S11); real protein complexes have correlated interfaces, so the scaling Smax ~ N^{1-2/n_c} may not transfer.
  • domain assumption In the retrieval regime assembly is effectively irreversible with no removals, so growth proceeds through N_tot max-rate addition events (Eq. 2).
    Used in Sec. V A and SI S4; SI S3 shows the assumption fails when removal rates compete, e.g. for δ > δ_blue ≈ μ/2, producing stall regimes.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Resolving Speed and Encoding Bottlenecks in Fast Heteromeric Self-Assembly." pith.science (2026). https://pith.science/paper/MWORPKVE

@misc{pith2026251116362,
  author       = {Pith},
  title        = {Pith review of: Resolving Speed and Encoding Bottlenecks in Fast Heteromeric Self-Assembly},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MWORPKVE}},
  note         = {Machine review of arXiv:2511.16362}
}
read the original abstract

The cytoplasm is a heterogeneous mixture containing many types of proteins that self-assemble into a wide variety of complexes. The accuracy and speed of cytoplasmic self-assembly is astonishing because it involves the correct identification of components shared among different structures, despite pervasive thermal fluctuations. Typical toy models of self-assembly are based on the specificity of binding energies among components. However, kinetics plays a key role in biological self-assembly, often catalyzed by a plethora of assembly factors. Building on this observation, we extend a previous heteropolymer growth model to describe the retrieval of two-dimensional structures via quasi-2D growth. We find that the self-assembly of structures in this model is subject to strong speed and encoding bottlenecks. Moreover, we show that these bottlenecks can be suppressed by increasing the connectivity of a small fraction of components. This mechanism of kinetically controlling a small number of critical binding events provides a simple explanation for the timely assembly of large protein, and suggests a unifying principle for the role of assembly factors.

Figures

Figures reproduced from arXiv: 2511.16362 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: F for S = 2 and Fig. S7 for S near Smax. However, [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

71 extracted references · 1 linked inside Pith

  1. [1]

    Denoting the multiplicity of correct and incorrect additions at critical events as Ω C and ΩI, we show in SI Sec. S4 that the minimum discrimination barrier necessary for accurate high-speed retrieval is δmin = 1 nc ln NcΩI ΩC .(4) For the simple scenario with connectivity z = 4 and a square target with side length ℓ = √ N [Fig. 3], we have that addition ...

  2. [2]

    Khatter, A

    H. Khatter, A. G. Myasnikov, S. K. Natchiar, and B. P. Klaholz, Structure of the human 80S ribosome, Nature 520, 640 (2015)

    2015

  3. [3]

    M. C. Wahl, C. L. Will, and R. L¨ uhrmann, The spliceo- some: Design principles of a dynamic RNP machine, Cell 136, 701 (2009)

    2009

  4. [4]

    S. S. Chen, E. Sperling, J. M. Silverman, J. H. Davis, and J. R. Williamson, Measuring the dynamics ofE. coli ribosome biogenesis using pulse-labeling and quantitative mass spectrometry, Mol. BioSyst.8, 3325 (2012)

    2012

  5. [5]

    D¨ orner, C

    K. D¨ orner, C. Ruggeri, I. Zemp, and U. Kutay, Ribosome biogenesis factors – from names to functions, EMBO J. 42, e112699 (2023)

    2023

  6. [6]

    Vercellino and L

    I. Vercellino and L. A. Sazanov, The assembly, regulation and function of the mitochondrial respiratory chain, Nat. Rev. Mol. Cell Biol.23, 141 (2022)

    2022

  7. [7]

    J. H. Davis and J. R. Williamson, Structure and dynamics of bacterial ribosome biogenesis, Phil. Trans. R. Soc. B 372, 20160181 (2017)

    2017

  8. [8]

    Rousseau and A

    A. Rousseau and A. Bertolotti, Regulation of proteasome assembly and activity in health and disease, Nat. Rev. Mol. Cell Biol.19, 697 (2018)

    2018

Show all 71 references
  1. [9]

    Altegoer and G

    F. Altegoer and G. Bange, Undiscovered regions on the molecular landscape of flagellar assembly, Curr. Opin. Microbiol.28, 98 (2015)

    2015

  2. [10]

    Seffouh, R

    A. Seffouh, R. Nikolay, and J. Ortega, Critical steps in the assembly process of the bacterial 50S ribosomal subunit, Nucleic Acids Res.52, 4111 (2024)

    2024

  3. [11]

    A. M. Mulder, C. Yoshioka, A. H. Beck, A. E. Bunner, R. A. Milligan, C. S. Potter, B. Carragher, and J. R. Williamson, Visualizing ribosome biogenesis: Parallel as- sembly pathways for the 30S subunit, Science330, 673 (2010)

    2010

  4. [12]

    Sheng, N

    K. Sheng, N. Li, J. N. Rabuck-Gibbons, X. Dong, D. Lyumkis, and J. R. Williamson, Assembly landscape for the bacterial large ribosomal subunit, Nat. Commun. 14, 5220 (2023)

    2023

  5. [13]

    Wild and P

    T. Wild and P. Cramer, Biogenesis of multisubunit RNA polymerases, Trends Biochem. Sci.37, 99 (2012)

    2012

  6. [14]

    H. M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. N. Bhat, H. Weissig, I. N. Shindyalov, and P. E. Bourne, The protein data bank, Nucleic Acids Res.28, 235 (2000)

    2000

  7. [15]

    Woolford, John L and S

    J. Woolford, John L and S. J. Baserga, Ribosome biogen- esis in the yeast saccharomyces cerevisiae, Genetics195, 643 (2013)

    2013

  8. [16]

    Lavdovskaiaet al., A roadmap for ribosome assembly in human mitochondria, Nat

    E. Lavdovskaiaet al., A roadmap for ribosome assembly in human mitochondria, Nat. Struct. Mol. Biol. (2024)

    2024

  9. [17]

    Heinz, P

    S. Heinz, P. Liauw, J. Nickelsen, and M. Nowaczyk, Analy- sis of photosystem II biogenesis in cyanobacteria, Biochim. Biophys. Acta - Bioenerg.1857, 274 (2016)

    2016

  10. [18]

    H. Yang, J. Liu, X. Wen, and C. Lu, Molecular mechanism of photosystem I assembly in oxygenic organisms, Biochim. Biophys. Acta - Bioenerg.1847, 838 (2015)

    2015

  11. [19]

    R¨ uhle and D

    T. R¨ uhle and D. Leister, Assembly of F1F◦−ATP syn- thases, Biochim. Biophys. Acta1847, 849 (2015)

    2015

  12. [20]

    J. P. Armitage and R. M. Berry, Assembly and dynamics of the bacterial flagellum, Annu. Rev. Microbiol.74, 181 (2020)

    2020

  13. [21]

    H. P. Erickson, Size and shape of protein molecules at the nanometer level determined by sedimentation, gel filtration, and electron microscopy, Biol. Proced. Online 11, 32 (2009)

    2009

  14. [22]

    Reuveni, M

    S. Reuveni, M. Ehrenberg, and J. Paulsson, Ribosomes are optimized for autocatalytic production, Nature547, 293 (2017)

    2017

  15. [23]

    A. E. Bunner, A. H. Beck, and J. R. Williamson, Kinetic cooperativity inE. coli30S ribosomal subunit recon- stitution reveals additional complexity in the assembly landscape, Proc. Natl. Acad. Sci. U.S.A.107, 5417 (2010)

    2010

  16. [24]

    J. R. Williamson, Cooperativity in macromolecular as- sembly, Nat. Chem. Biol.4, 458 (2008)

    2008

  17. [25]

    E. S. Chhabra and H. N. Higgs, The many faces of actin: matching assembly factors with cellular structures, Nature Cell Biology9, 1110 (2007)

    2007

  18. [26]

    von der Ecken, M

    J. von der Ecken, M. M¨ uller, W. Lehman, D. J. Manstein, P. A. Penczek, and S. Raunser, Structure of the F-actin– tropomyosin complex, Nature519, 114 (2015)

    2015

  19. [27]

    Fellous, J

    A. Fellous, J. Francon, A.-M. Lennon, and J. Nunez, Microtubule assembly in vitro, European Journal of Bio- chemistry78, 167 (1977)

    1977

  20. [28]

    M. G. Mateu, Assembly, stability and dynamics of virus capsids, Archives of Biochemistry and Biophysics531, 65 (2013)

    2013

  21. [29]

    Kurisaki and S

    I. Kurisaki and S. Tanaka, Computational prediction of heteromeric protein complex disassembly order using hy- brid monte carlo/molecular dynamics simulation, Phys. Chem. Chem. Phys.24, 10575 (2022)

    2022

  22. [30]

    F. M. Gartner and E. Frey, Design principles for fast and efficient self-assembly processes, Phys. Rev. X14, 021004 (2024)

    2024

  23. [31]

    Lenz and T

    M. Lenz and T. Witten, Geometrical frustration yields fi- bre formation in self-assembly, Nat. Phys.13, 1100 (2017)

    2017

  24. [32]

    V. N. Manoharan, Colloidal matter: Packing, geometry, and entropy, Science349, 1253751 (2015). 10

    2015

  25. [33]

    Ravasio, K

    R. Ravasio, K. Husain, C. G. Evans, R. Phillips, M. Ribezzi, J. W. Szostak, and A. Murugan, A minimal scenario for the origin of non-equilibrium order (2024), arXiv:2405.10911 [q-bio.PE]

    2024 arXiv

  26. [34]

    Murugan, Z

    A. Murugan, Z. Zeravcic, M. P. Brenner, and S. Leibler, Multifarious assembly mixtures: Systems allowing re- trieval of diverse stored structures, Proc. Natl. Acad. Sci. U.S.A.112, 54 (2015)

    2015

  27. [35]

    Sartori and S

    P. Sartori and S. Leibler, Lessons from equilibrium statis- tical physics regarding the assembly of protein complexes, Proc. Natl. Acad. Sci. U.S.A.117, 114 (2020)

    2020

  28. [36]

    Benoist and P

    F. Benoist and P. Sartori, High-speed combinatorial poly- merization through kinetic-trap encoding, Phys. Rev. Lett. 134, 038402 (2025)

    2025

  29. [37]

    K. A. Dill, K. M. Fiebig, and H. S. Chan, Cooperativity in protein-folding kinetics, Proc. Natl. Acad. Sci. U.S.A. 90, 1942 (1993)

    1942

  30. [38]

    C. H. Bennett, Dissipation-error tradeoff in proofreading, Biosystems11, 85 (1979)

    1979

  31. [39]

    Sartori and S

    P. Sartori and S. Pigolotti, Kinetic versus energetic dis- crimination in biological copying, Phys. Rev. Lett.110, 188101 (2013)

    2013

  32. [40]

    Tsai and K

    Y.-C. Tsai and K. A. Johnson, A new paradigm for DNA polymerase specificity, Biochemistry45, 9675 (2006)

    2006

  33. [41]

    Benoist, L

    F. Benoist, L. Peliti, and P. Sartori, Content-addressable memory with a content-free energy function (2025), arXiv:2503.18822 [cond-mat.stat-mech]

    2025

  34. [42]

    Gavinet al., Proteome survey reveals modularity of the yeast cell machinery, Nature440, 631 (2006)

    A.-C. Gavinet al., Proteome survey reveals modularity of the yeast cell machinery, Nature440, 631 (2006)

    2006

  35. [43]

    K¨ uhneret al., Proteome organization in a genome- reduced bacterium, Science326, 1235 (2009)

    S. K¨ uhneret al., Proteome organization in a genome- reduced bacterium, Science326, 1235 (2009)

    2009

  36. [44]

    Osat and R

    S. Osat and R. Golestanian, Non-reciprocal multifarious self-organization, Nat. Nanotechnol.18, 79 (2023)

    2023

  37. [45]

    Whitelam, L

    S. Whitelam, L. O. Hedges, and J. D. Schmit, Self- assembly at a nonequilibrium critical point, Phys. Rev. Lett.112, 155504 (2014)

    2014

  38. [46]

    Nguyen and S

    M. Nguyen and S. Vaikuntanathan, Design principles for nonequilibrium self-assembly, Proc. Natl. Acad. Sci. U.S.A.113, 14231 (2016)

    2016

  39. [47]

    Chen and W

    F. Chen and W. M. Jacobs, Dynamical phase transition in the growth of programmable polymorphic materials, Phys. Rev. Mater.9, 053403 (2025)

    2025

  40. [48]

    Bisker and J

    G. Bisker and J. L. England, Nonequilibrium associative retrieval of multiple stored self-assembly targets, Proc. Natl. Acad. Sci. U.S.A.115, E10531 (2018)

    2018

  41. [49]

    Bupathy, D

    A. Bupathy, D. Frenkel, and S. Sastry, Temperature pro- tocols to guide selective self-assembly of competing struc- tures, Proc. Natl. Acad. Sci. U.S.A.119, e2119315119 (2022)

    2022

  42. [50]

    Holmes-Cerfon and M

    M. Holmes-Cerfon and M. Wyart, Hierarchical self- assembly for high-yield addressable complexity at fixed conditions, Proc. Natl. Acad. Sci. U.S.A.122, e2500245122 (2025)

    2025

  43. [51]

    R. B. Teixeira, G. Carugno, I. Neri, and P. Sartori, Liquid Hopfield model: Retrieval and localization in multicompo- nent liquid mixtures, Proc. Natl. Acad. Sci. U.S.A.121, e2320504121 (2024)

    2024

  44. [52]

    W. M. Jacobs, Self-assembly of biomolecular condensates with shared components, Phys. Rev. Lett.126, 258101 (2021)

    2021

  45. [53]

    J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, Proc. Natl. Acad. Sci. U.S.A.79, 2554 (1982)

    1982

  46. [54]

    Krotov and J

    D. Krotov and J. J. Hopfield, Dense associative memory for pattern recognition, inAdvances in Neural Informa- tion Processing Systems, Vol. 29 (Curran Associates, Inc., 2016)

    2016

  47. [55]

    Ramsaueret al., Hopfield networks is all you need, inInternational Conference on Learning Representations (2021)

    H. Ramsaueret al., Hopfield networks is all you need, inInternational Conference on Learning Representations (2021)

    2021

  48. [56]

    Whitelam and R

    S. Whitelam and R. L. Jack, The statistical mechanics of dynamic pathways to self-assembly, Annu. Rev. Phys. Chem.66, 143 (2015)

    2015

  49. [57]

    McMullen, M

    A. McMullen, M. Mu˜ noz Basagoiti, Z. Zeravcic, and J. Brujic, Self-assembly of emulsion droplets through pro- grammable folding, Nature610, 502 (2022)

    2022

  50. [58]

    Banerjee, A

    K. Banerjee, A. B. Kolomeisky, and O. A. Igoshin, Elu- cidating interplay of speed and accuracy in biological error correction, Proc. Natl. Acad. Sci. U.S.A.114, 5183 (2017)

    2017

  51. [59]

    Pigolotti and P

    S. Pigolotti and P. Sartori, Protocols for copying and proofreading in template-assisted polymerization, J. Stat. Phys.162, 1167 (2016)

    2016

  52. [60]

    P. Yin, H. M. T. Choi, C. R. Calvert, and N. A. Pierce, Programming biomolecular self-assembly pathways, Na- ture451, 318 (2008)

    2008

  53. [61]

    J. J. Hopfield, Kinetic proofreading: A new mechanism for reducing errors in biosynthetic processes requiring high specificity, Proc. Natl. Acad. Sci. U.S.A.71, 4135 (1974)

    1974

  54. [62]

    Lefebvre and C

    B. Lefebvre and C. Maes, Frenetic steering in a nonequi- librium graph, J. Stat. Phys.190, 90 (2023)

    2023

  55. [63]

    Andrieux and P

    D. Andrieux and P. Gaspard, Nonequilibrium generation of information in copolymerization processes, Proc. Natl. Acad. Sci. U.S.A.105, 9516 (2008)

    2008

  56. [64]

    Koehler, P

    L. Koehler, P. Ronceray, and M. Lenz, How do particles with complex interactions self-assemble?, Phys. Rev. X 14, 041061 (2024)

    2024

  57. [65]

    J. R. Warner and K. B. McIntosh, How common are ex- traribosomal functions of ribosomal proteins?, Molecular Cell34, 3 (2009)

    2009

  58. [66]

    Alberts, A

    B. Alberts, A. Johnson, J. Lewis, D. Morgan, M. Raff, K. Roberts, and P. Walter, How cells read the genome: From DNA to protein. In: Molecular biology of the cell (Garland Science, New York, 2015) pp. 299–368, 6th ed

    2015

  59. [67]

    M. Bai, X. Zhao, K. Sahara, Y. Ohte, Y. Hirano, T. Kaneko, H. Yashiroda, and S. Murata, In-depth analy- sis of the lid subunits assembly mechanism in mammals, Biomolecules9(2019)

    2019

  60. [68]

    Q.-Z. Zhu, C. X. Du, E. M. King, and M. P. Brenner, Proofreading mechanism for colloidal self-assembly, Phys. Rev. Res.6, L042057 (2024)

    2024

  61. [69]

    B. Wei, M. Dai, and P. Yin, Complex shapes self- assembled from single-stranded DNA tiles, Nature485, 623 (2012)

    2012

  62. [70]

    C. G. Evans, J. O’Brien, E. Winfree, and A. Murugan, Pattern recognition in the nucleation kinetics of non- equilibrium self-assembly, Nature625, 500 (2024)

    2024

  63. [71]

    Resolving Speed and Encoding Bottlenecks in Fast Heteromeric Self-Assembly

    R. D. Barish, R. Schulman, P. W. K. Rothemund, and E. Winfree, An information-bearing seed for nucleating algorithmic self-assembly, Proc. Natl. Acad. Sci. U.S.A. 106, 6054 (2009). 1 Supporting information for “Resolving Speed and Encoding Bottlenecks in Fast Heteromeric Self-...

    2009

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.